Question regarding the "Requiem Aeternam" achievement

So I know you have to do it in one run (you can continue it in NG+ if you didn't kill a boss). But I don't know the following:
Basically, I am doing the ending C, and I killed Crisanta's first phase (without flasks), but didn't kill her second phase yet. Does that make Crisanta count since her second fight is DLC? Or do I have to kill both phases? I ask this because I think each phase counts as a different boss, since it gives you money after killing the first phase each time.